Solute characterization by optoelectronkinetic potentiometry in an inclined array of optical traps

ABSTRACT

A method and apparatus for selecting a specific fraction from a heterogeneous fluid-borne sample using optical gradient forces in a microfluidic or fluidic system are presented. Samples may range in size from a few nanometers to at least tens of micrometers, may be dispersed in any fluid medium, and may be sorted on the basis of size, shape, optical characteristics, charge, and other physical properties. The selection process involves passive transport through optical intensity field driven by flowing fluid, and so offers several advantages over competing techniques. These include continuous rather than batch-mode operation, continuous and dynamic tunability, operation over a wide range of samples, compactness, and low cost.

The present invention was supported by the National Science Foundationunder Grant Number DBI-0233971, with additional support from GrantNumber DMR-0304906.

FIELD OF THE INVENTION

The present invention relates to modulated optical tweezers. Moreparticularly, the present invention relates to the use of modulatedoptical tweezers in a variety of situations.

BACKGROUND OF THE INVENTION

Since their introduction a decade ago, optical tweezers have becomeindispensable tools for physical studies of macromolecular andbiological systems. Formed by bringing a single laser beam to a tightfocus, an optical tweezer exploits optical gradient forces to manipulatemicrometer-sized objects. Optical tweezers have allowed scientists toprobe the small forces that characterize the interactions of colloids,polymers and membranes, and to assemble small numbers of colloidalparticles into mesoscopic structures. Conventional efforts each requiredonly one or two optical tweezers. Extending these techniques to largerand more complex systems requires larger and more complex arrays ofoptical traps.

Related techniques for creating multiple simultaneous optical trapsinclude the generalized phase contrast method, interferometric opticaltweezers, and optical lattices. The latter two approaches involveinterfering multiple beams in the volume of the sample, while the formermight be considered a variant of holographic optical trapping.Interferometric techniques can cover larger areas than holographictechniques, but are substantially more limited in the types of intensitypatterns that can be created. In particular, interferometric opticaltweezers and optical lattices are limited to periodic structures.

A single laser beam brought to a focus with a strongly converging lensforms a type of optical trap widely known as an optical tweezer. Ingeneral, such a beam can be described by a wave function,ψ(r)=A(r)exp(iφ(r))  (1)

where A(r) is the amplitude profile and φ(r) is the phase at position rin a plane transverse to the optical axis.

A conventional optical tweezer is created from the TEM₀₀ laser beamprovided by a typical laser. Such a beam's wave fronts are planar andcan be described by the uniform phase profile φ(r)=φ0. Bringing such abeam to a diffraction-limited focus with an appropriate focusingelement, such as a microscope objective lens, transforms the beam intoan optical tweezer. The position of the optical tweezer in the lens'focal plane is determined by the angle at which the team enters thelens' input pupil. Additionally, if the beam is diverging as it entersthe input pupil, it comes to a focus and forms an optical tweezerdownstream of the focal plane. Alternatively, if the beam is converging,it forms a trap upstream of the focal plane.

Multiple beams of light passing simultaneously through the lens inputpupil yield multiple optical tweezers, each at a location determined bythe angle of incidence arid degree of collimation at the input pupil.These beams form an interference pattern as they pass through the inputpupil, whose amplitude and phase corrugations characterize thedownstream trapping pattern. Imposing the same modulations on a singleincident beam at the input pupil would yield the same pattern of traps,but without the need to create and direct a number of independent inputbeams. Such wave front modification can be performed by a type ofdiffractive optical element (DOE) commonly known as a hologram.Generally, the hologram or DOE encoding a particular pattern of opticaltraps can be calculated with a computer through a procedure known ascomputer-generated holography (CGH). Using CGH to create arbitraryconfigurations of multiple optical traps constitutes a new class ofoptical micromanipulation tools known as holographic optical tweezers(HOT), with manifold applications in the physical and biologicalsciences as well as in industry.

The efficacy of holographic optical tweezers is determined by thequality of the trap-forming DOE, which in turn reflects the performanceof the numerical algorithms used in their computation. Previous studieshave applied holograms calculated by simple linear superposition of theinput fields or with variations on the classic Gerchberg-Saxton andAdaptive-Additive algorithms. Despite their general efficacy, thesealgorithms yield traps whose relative intensities can differsubstantially from their design values, and typically result inundesirable “ghost” traps. These problems can become acute forcomplicated three dimensional trapping patterns, particularly when thesame hologram also is used as a mode converter to projectmultifunctional arrays of optical traps.

The holograms used for holographic optical trapping typically operateonly on the phase of the incident beam, and not its amplitude. Suchphase-only holograms, also known as kinoforms, are far more efficientthan amplitude-modulating holograms, which necessarily divert light awayfrom the beam. They also are substantially easier to implement thanfully complex holograms that would be required to create arbitrarysuperpositions at the input pupil. Indeed, sequences of kinoforms can beprojected with a computer-addressed spatial light modulator (SLM) tocreate dynamic holographic optical tweezers.

General trapping patterns can still be achieved with kinoforms despitethe loss of information that might be encoded in amplitude modulationsbecause optical tweezers rely for their operation on intensity gradientsand not local phase variations. However, it is still necessary to finda. pattern of phase shifts in the input plane that encodes the desiredintensity pattern in the focal volume.

SUMMARY OF THE INVENTION

The present invention relates a variant of optical tweezers in which thetrap's stiffness is made to vary with direction. In particular, themodified trap's intensity spreads more broadly in selected directions,thereby reducing its stiffness in those directions, or facilitatingalignment of asymmetric objects along those directions. Such modifiedtraps may be used to facilitate objects' escape along selecteddirections and to orient and rotate non-compact objects. The ability tofacilitate objects' escape along selected directions has applicationsfor optical fractionation, in which objects' differing interactions withoptical traps are used as the basis for sorting. The ability to orientand rotate non-compact objects may be used in assemblingmicrometer-scale objects.

Previously reported methods for orienting objects in optical trapsinclude creating optical tweezers from Gauss-Hermite modes, modifyingtheir amplitude profiles with rectangular apertures, rotating thepolarization angle of linearly and elliptically polarized light,interfering Laguerre-Gaussian modes with plane waves to create symmetricspiral patterns, modulating normally circular optical vortices andprojecting multiple conventional optical tweezers in close proximity.

The present invention also relates to a new class of algorithms for HOTCGH calculation based on direct search and simulated annealing that takeadvantage of recently introduced metrics to achieve unprecedentedtrap-formation accuracy and optical efficiency.

The present invention is preferably implemented through holographicoptical trapping, but also can be implemented with other relatedtechniques such as the generalized phase contrast method,interferometric optical tweezers, and optical lattices.

One implementation of the invention is an apparatus for selectingfractions through optical fractionation that includes at least twochannels for providing at least first and second laminar fluid flows,respectively. At least one of the two fluid flows contains fluid-borneparticles. A holographic optical tweezer system projects at least twooptical arrays of optical traps onto a region at a junction of at leastthe two channels. The two arrays of optical traps each selectivelydeflect the fluid-borne particles for fractionating the fluid-borneparticles according to a characteristic of the fluid-borne particles.

Another implementation of the invention is an apparatus for selectingfractions through optical fractionation, including N channels forproviding N laminar input streams. At least one of the N laminar inputstreams contains fluid-borne particles. A holographic optical tweezersystem projects an optical array on a region of a junction of thechannels to fractionate the fluid-borne particles in the N laminar inputstreams into M laminar output streams, where N does not necessarilyequal M.

The present invention also relates to methods for creating holographicoptical traps with two separate input lasers, with applicationsincluding creating holographic optical traps (HOTs) with two wavelengthsof light. These methods can be extended to include more than two inputlasers.

In addition, the present invention describes a method for characterizingseveral aspects of a solute's charge state, size, size polydispersity,and other properties as it is driven by flowing solvent through an arrayof optical traps inclined with respect to the flow direction.

These and other objects, advantages and features of the invention,together with the organization and manner of operation thereof, willbecome apparent from the following detailed description when taken inconjunction with the accompanying drawings, wherein like elements havelike numerals throughout the several drawings described below.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows modulated optical tweezer, wherein the left panel shows theunmodulated intensity profile of a conventional optical tweezer createdfrom a beam with a flat-top profile at a distance z=5λ from the focus,where λ is the wavelength of light, and wherein the right panel shows anequivalent cross-section through a beam sinusoidally modulated accordingto φ({right arrow over (r)})=α_(m) sin(mθ−θ_(m)) with m=5, α_(m)=1, andθ_(m)=0.

FIG. 2 shows a three-dimensional multifunctional holographic opticaltrap array created with a single phase-only DOE computed with the directsearch algorithm, wherein the top DOE phase pattern includes whiteregions corresponding to a phase shift of 2π radians and black regionscorresponding to 0, and wherein the bottom projected optical trap arrayis shown at z=−10 μm, 0 μm and +10 μm from the focal plane of a 100×, NA1.4 objective lens, with the traps being spaced by 1.2 μm in the plane,and the 12 traps in the middle plane consisting of l=8 optical vortices;

FIG. 3 is a plot showing performance metrics for the algorithm thatcalculated the hologram in FIG. 2 as a function of the number ofaccepted single-pixel changes;

FIG. 4 shows an H-junction having a plurality of laminar input streamscoming together into a single interaction region and then separatinginto a plurality of output streams;

FIG. 5 shows an embodiment of the present invention in which a singleinput sample is dispersed into several discrete fractions;

FIG. 6 shows an embodiment of the present invention in which mixingcomponents of two or more input streams creates a single thoroughlymixed output streams.

FIG. 7 is an illustration in which two or more input streams are mixedto create a single, thoroughly mixed, output stream;

FIG. 8 is a representation of one method for creating two-colorholographic optical traps according to one embodiment of the presentinvention;

FIG. 9 is a representation of a second method for creating two-colorholographic optical traps according to one embodiment of the presentinvention;

FIG. 10 is a representation of a third method for creating two-colorholographic optical traps according to one embodiment of the presentinvention;

FIG. 11 is a representation of a fourth method for creating two-colorholographic optical traps according to one embodiment of the presentinvention;

FIG. 12 is a schematic diagram of a practical implementation ofoptoelectrokinetic potentiometry; and

FIG. 13 is a plot showing the transverse velocity ν_(⊥) relative to flowspeed ν, of 1.5 μm diameter silica spheres dispersed in water, as afunction of an orientation angle Θ of a 10×10 array of holographicoptical tweezers, wherein the two data sets shown were obtained fordifferent values of the flow speed u.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Optical traps refer to a type of force exerted by a beam of light totrap and move small objects. In general, these forces fall into twocategories: (1) radiation pressure that tends to push objects down theaxis of a beam, and (2) optical gradient forces. Optical gradient forcesarise because objects develop electromagnetic dipole moments whenilluminated by light. Intensity gradients in the light exert forces onthese dipole moments whose sign depends on the relative dielectricconstants of the object and the surrounding medium. Particles withhigher dielectric constants than their surroundings (high-dielectricparticles) generally are drawn up by the gradients toward brighterregions while low-dielectric particles are pushed away to darkerregions.

Optical gradient forces provide the basic forces necessary for thesingle-beam optical trap known as an optical tweezer. An optical tweezercomprises a single beam of light brought to a diffraction-limited focusby a high-numerical aperture lens, such as a microscope objective lens.High-dielectric objects are drawn toward the focal point, where thelight is most intense. At the same time, they are repelled by radiationpressure that tends to drive them downstream. If the gradient forcesdominate, the particles can be stably trapped somewhere near the focalpoint.

In other words, the focused beam of light provides a three-dimensionalpotential energy well for high-dielectric particles, and a potentialenergy barrier for particles that are repelled by the light. The latterclass of particles repelled by radiation pressure includeslow-dielectric particles, as well as particles that strongly absorb orreflect the focused light. All of these effects can be enhanced andmodified if the wavelength of light is near a resonance of the particle.

A single beam of light brought to a single focus creates a singleoptical tweezer, and therefore, a single localized potential well. Theholographic optical tweezer technique creates multiple simultaneousindependent optical tweezer from a single beam of light and a singlefocusing element. Consequently, holographic optical tweezers can createany desired three dimensional arrangement of potential energy wells orbarriers.

Creating multiple holographic optical traps applies the same basicoptical principles used to create a single optical tweezer. Inparticular, a collimated beam of light coaxial with the optical axis ofa focusing element, such as an infinity-corrected objective lens, isbrought to a focus in the middle of the focusing element's focal plane,and forms a trap accordingly. A collimated beam entering the focusingelement's entrance pupil at an angle comes to a focus in the focalplane, but at a point displaced from the optical axis by an amount thatdepends on the angle of incidence and in a direction that depends on thedirection of the tilt. Changing the angle of incidence therefore changesthe location of the resulting trap in the focal plane of the focusingelement, and allows the trap to be translated in two dimensions.Changing the beam's degree of collimation moves the trap in the thirddimension, along the optical axis. A slightly diverging beam passingthrough the entrance pupil comes to a focus downstream of the focalplane, while a slightly converging beam comes to a focus upstream. Theaxial displacement of the focal point depends on the degree ofcollimation. Controlling both the angle of incidence and degree ofcollimation of the beam as it passes through the focusing element'sentrance pupil therefore controls the position of the resulting opticaltweezer in three dimensions, with a single input beam resulting in asingle trap.

Several beams of light all passing through the focusing element'sentrance pupil at different angles and with different degrees ofcollimation would form multiple optical traps at different positions inthe focusing element's focal volume. If all of the beams have the samewavelength, they could be derived from the same source. Creatingmultiple simultaneous traps, therefore, requires a method for creatingmultiple beams all propagating in particular directions, each with itsown specific degree of collimation, and all passing through the entrancepupil of the focusing element. Holographic optical trapping solves thisproblem in a very general way, as described in U.S. Pat. Nos. 6,055,106;6,416,190; 6,624,940; 6,626,546; and 6,639,208, all of which areincorporated herein by reference.

Multiple coherent beams of light passing through the plane of theentrance pupil form an interference pattern composed of spatialvariations in light amplitude and phase. A single beam of lightimprinted with the same variations would propagate in the same way asthe multiple beams—this is the principle of holography. A device thatimprints the particular modulation required to transform a single beaminto a desired fan-out of beams may be said to project the associatedhologram. More specifically, a device commonly known as a diffractivebeam splitter, a holographic beam splitter, or a kinoform constitutes anexample of a diffractive optical element (DOE) that can be used tocreate holographic optical traps.

Placing the appropriate hologram in the entrance pupil of the focusingelement, or in a plane conjugate to the entrance pupil, transforms asingle input beam of light into many beams, all passing through thefocusing element's entrance pupil. Each beam can have a specified angleof incidence and a specified degree of collimation. Consequently, eachforms an independent trap in the focal volume.

The resulting pattern of traps is specified by the hologram. Thehologram, in turn, can be implemented in many ways. Most preferably, theholograms can be designed by computers to create specific patterns oftraps.

This design process must take into consideration factors such as theamplitude profile of the input beam. Modulating the amplitude of a beamof light generally involves diverting energy out of the beam, either byabsorption or by reflection. In the former case, the absorbed light willtend to heat the absorber, limiting the amount of power that can be usedto create the traps. In either case, the diverted light reduces theefficiency by which a single beam of light can be used to createmultiple traps, each of which requires a certain intensity to operate asdesired. In many cases, a desired pattern of optical traps can becreated by modulating only the phase profile of the input beam, and notits amplitude profile. This flexibility is available because opticaltrapping relies on the intensity of the trapping light, and thus on theamplitude, but not on the phase. As a result, infinitely many differentpatterns of phase modulation at the input plane of the focusing lensyield the same intensity distribution in the output plane for a givenamplitude profile. Consequently, a phase modulation can be chosen tocreate the desired pattern of traps without diverting energy from thebeam. The resulting phase-only DOE can be implemented through variationsin the thickness of a transparent medium such as glass, through thesurface relief of a mirror, or by controlling the index of refraction ofa medium such as a liquid crystal layer through which the light passes.

A computer-designed phase-only DOE can be implemented with a device ormedium whose relevant optical properties can be deliberately changed sothat the hologram it encodes can be updated accordingly. Such a dynamicimplementation of a trap-forming DOE can be used to update the beampattern in real time so that the resulting trapping pattern can bechanged. This transforms conventional holographic optical traps intodynamic holographic optical traps.

Holographic optical tweezers can project any desired pattern ofpotential wells or barriers into a transparent medium. This capabilitycan be combined with properties of fluids flowing at low Reynoldsnumbers to create a method for sorting fluid-borne objects. This sortingby light is referred to as optical fractionation. The basic opticalfractionation technique is based on holographic optical trapping and isdisclosed in published U.S. Patent Application 2003/0047676, which isincorporated herein by reference.

Fluids flowing at low Reynolds numbers undergo smooth laminar flow andtherefore undergo no mixing. Such flows can be achieved by reducing thedimensions of a channel through which the fluid passes, by reducing theflow speed, or by some combination of approaches. The field ofmicrofluidics is based on this principle. Consider two laminar streamscoming together at a junction-between two channels. If the resultingflow still maintains a low enough Reynolds number, the two streamscannot mix, but rather flow side-by-side separately, even if theyconsist of the same fluid. Eventually two miscible streams will mixthrough interdiffusion, but this can require a substantial interval.Before this happens, the two streams can be separated again intoseparate channels. A set of channels that brings two streams together,allows them to flow together for a period and then separates them againis known as an H-junction.

H-junctions are useful for sorting fluid-borne objects. An objectcarried along in one of the streams generally will continue in thatstream and come out the other side of the junction still in its stream.However, if the object diffuses or otherwise makes its way across theinterface between the two flows, then it will be collected in the otherstream at the output of the H-junction. Consider two streams entering anH-junction, one containing a heterogeneous sample and the othercontaining an empty buffer fluid. Any object crossing the H-junction'sinterface will be carried away by the buffer, and can be collected. Ifsome of the objects in the mixture are more diffusive than others, themore diffusive objects will cross the interface preferentially and willbe collected with higher efficiency than the others. Similarly, theinitial flow will be relatively enriched in the less-diffusive fractionupon exiting the H-junction.

This approach has at least three shortcomings. Macromolecular samplesdiffuse relatively slowly, so that effective separations requireH-junctions with substantial interfacial areas. Furthermore, the mostdiffusive fraction can do no better than spread throughout the bufferand sample flows. This limits the ultimate separation efficiency for asingle pass through an H-Junction. Finally, an object's diffusioncoefficients tend to depend only linearly on their size, so thatfractionation in H-junctions is unlikely to offer the resolutionrequired to separate fractions that differ only slightly from eachother. Optical fractionation overcomes these deficiencies while adding aspectrum of other advantages.

When a fluid-borne object encounters an array of optical traps, thetraps can act as potential energy wells. When the maximum trapping forceis comparable to the maximum driving force, objects interact stronglywith the traps but do not end up localized in them. Under thesecircumstances, the flowing particle's trajectory can be deflected enoughby its encounter with one trap that it falls into the domain ofinfluence of the next trap in the array. If the traps in the array areevenly spaced, and if the array is not aligned with the driving force,then the particle's trajectory can be systematically deflected away fromthe driving force's direction. The particle then selects a directionthat is commensurate with a symmetric direction through the array, butnot aligned with the driving force. Such a trajectory is said to belocked in to the array.

Different objects interact differently with the same pattern of opticaltraps, so that the potential energy landscape that a given objectexperiences in an array of traps depends on its properties.Consequently, different objects with different properties driven by thesame force through the same array of optical traps need not follow thesame trajectory. In particular, one type of object can become locked into the array under the same conditions that another type of object canescape. The locked-in class therefore is systematically deflected by thearray, while the other is not.

In the situation where the array of traps is placed across the sampleflow in a microfluidic H-junction, those objects that become locked into the array are deflected across the interface between the two flowsand can be collected in the buffer. Objects that escape the array willbe retained by the sample stream.

At a minimum, the modulated potential energy landscape provides amechanism to tune the transfer of fluid borne objects across theinterface of an H-junction and thereby provides a degree of optimizationnot otherwise available. Moreover, a distinction between locked-in andfree states can depend with exponential sensitivity on an object's size,and thus this distinction qualitatively surpasses the sensitivityoffered by diffusion alone. Furthermore, because optical fractionationcan be accomplished over the extent of a small array of traps, longH-junctions are not required.

Which fraction is deflected by an array of optical tweezers isdetermined by the separation between traps, the symmetry of the array,the intensity of the traps, the angle of inclination, and the wavelengthof light used. All of these characteristics can be changed dynamicallyto optimize the selection for a particular fraction. These also areadvantages, therefore, over separation by diffusion alone. Furthermore,optical trapping has been demonstrated for objects as small as 5nanometers and as large as several hundred micrometers. Thus, opticalfractionation is useful over this entire size range. The same physicalapparatus, moreover, can be used over the entire range. This is asubstantial advantage over all other known sorting techniques. Finally,arrays can be designed so that every object satisfying the lock-incriterion is deflected across the interface. Nearly perfect sorting cantherefore be achieved with a single line of traps inclined with respectto the flow, spanning the sample stream and extending slightly into thebuffer stream.

Although the following discussion focuses on fractionation by size, thesame principles may also be applied to sorting on the basis of otherproperties as well. The fraction selected by a particular array includesall objects of a certain size and above. In many applications, only aparticular size range might be required. Or, conversely, it might benecessary to remove a particular size range from a sample, for instance,to create a bimodal distribution. This could be implemented with twopasses through single-stage optical fractionation systems, one to removethe fraction that is too large, and the other to pick off the desiredfraction. However, these two steps can be combined through the use of asingle appropriately designed array of traps projected into a singleH-junction as shown in FIG. 4. This is referred to as multi-stage ormulti-functional optical fractionation. Several variants of thisapproach will be described below, as is a basic method for selectingmultiple fractions simultaneously.

FIG. 4 shows a first variant of the basic method in which particles oftypes P1, P2 and P3 are carried by a sample stream 105 into anH-junction 100. When the flow passes through a first manifold of opticaltraps 110A, all particles of a particular size and larger, for example,P1 and P2, are swept into the buffer stream 120. If the buffer stream120 now encounters a second array of traps 110B designed to deflect someof the first fraction, for example, P1, back into the sample stream,then the remaining fraction in the buffer stream includes only particlesof a particular specified size range, P2. The second array of traps canbe projected with the same DOE that created the initial array, and thuscan use the same laser. More generally, the second array can be createdwith a second DOE that also is conjugate to the focusing element'sentrance pupil, with a single DOE specially designed to create twodistinct trapping patterns from the two different wavelengths of light.

The net effect is that two distinct optical trap arrays 110A and 110Bare projected into the same H-junction 100 such that the first sweepsboth the desired fraction and another undesired fraction across theinterface and the second sweeps the undesired fraction back into theinitial sample stream. The result is that the buffer stream 120 exitingthe H-junction contains only the selected fraction P2, and the samplestream contains everything else, P1 and P3.

An H-junction 400 can be generalized to include a number N of laminarinput streams 410 coming together into a single interaction region 420and then separating into M output streams 430, as shown in FIG. 5. Ingeneral, N does not have to equal M. A single pattern of optical trapsspanning the multi-stream interaction region 420 and taking the form ofmultiple arrays, therefore, can transfer fractions of an initial sampledistributed in any of the input streams into any of the output streams.The optical intensity pattern in this case may be thought of as aswitching yard, shuttling in-flowing objects into desired outgoingstreams. Because the pattern of traps can be changed by updating thetrap-forming DOE(s), which fraction finds its way to which output streamcan be altered and optimized dynamically.

One example of the invention is a variation of chromatography 500 inwhich a single input sample 510 is dispersed into several discretefractions 520 as shown in FIG. 6, each of which can be collectedseparately. This can be accomplished most simply with a single array oftweezer 530 whose geometric distribution changes discretely orcontinuously as it crosses the interfaces between output streams.

Another example would be mixing the components of two or more inputstreams to create a single thoroughly mixed output streams. This isillustrated in FIG. 7. Particles of types P1, P2, and P3 from inputstreams 610 are mixed at an interaction region 620, where an array ofoptical traps is projected, to come out into a single output stream 630.Such mixing is difficult in microfluidic systems whose strength is theirfreedom from mixing. Operating optical fractionation in reverse providesa system for dynamically and selectively mixing samples in microfluidicsystems.

Other examples arise from the combinatorial nature of the describedswitching and might include embodiments for drug testing in whichmicrobes are transferred through streams of drug candidates andindividually selected based on their responses. The benefit of thisapproach is that early-stage testing could proceed on vanishingly smallsamples by gauging their influence on individual microbes.

Other possible examples include selecting the precipitated products ofreactions ongoing in the streams, for example to retain products of acertain size or with particular optical properties. These products thencan be transferred into additional flows to facilitate multi-stepreactions, fabricating core-shell nanoparticles providing one example.Because this process can proceed continuously, it may provide the basisfor manufacturing such products in quantity. The benefit here overwet-chemistry methods is the generic ability to optimize the productwithout regard to chemical kinetics.

The present invention also involves a particular class of modificationsto ψ(r) that lead to a number of useful properties. In particular, thisinvolves the class of modulated phase profiles,φ(r)=α_(m) sin(mθ−θ _(m))  (2)where θ is the azimuthal angle around the optical axis, m is the indexcorresponding to an m-fold sinusoidal modulation, and αm is theassociated depth of modulation. The phase angle θ_(m) can be used torotate the entire pattern relative to the reference direction. Moregeneral profiles can be constructed using Fourier's theorem:

$\begin{matrix}{{\varphi(r)} = {\sum\limits_{m = 0}^{\infty}{\alpha_{m}{{\sin( {m\;\theta} )}.}}}} & (3)\end{matrix}$

Eqs. (2) and (3) introduce controlled m-fold aberrations into theincident beam. The aberrations tend to blur the focus along selecteddirections, thereby extending the intensity distribution along thosedirections, and reducing the intensity gradients along those directions.This effect is shown in FIG. 1. The extension of the intensitydistribution is useful for orienting extended objects. The reduction ofthe intensity gradients selectively weakens optical gradient forcetrapping along those directions.

When orienting extended objects, the phase structure from Eq. (3) isselected to fit the profile of the object to be oriented. Onceprojected, this pattern will tend to orient the extended object asdesired.

For applications in optical fractionation, individual optical traps canbe selectively weakened in desired directions. These directions may bealigned with the lattice directions of the array of traps, with thedirection of the force-driving objects through the array or in someother direction. The modulation's profile and depth can be selected tooptimize transport of selected objects through the array, particularlyin cases where such leakage can improve the process' selectivity.

The profiles described by Eqs. (2) and (3) can be combined with othermode-forming and trap-generating phase functions to create other typesof modulated optical traps and to place them selectively in threedimensions. The present invention separates the notion of modulating theintensity profile from the notion of generating helical modes of light,and thereby facilitates applications that do not rely on the propertiesof helical modes.

Implementing these and other applications of holographic optical trapsrequires accurate and efficient methods for computing the necessaryphase patterns. According to scalar diffraction theory, the (complex)field E({right arrow over (r)}) in the focal plane of a lens of focallength ƒ is related to the field, u({right arrow over (ρ)})exp(iφ({rightarrow over (ρ)})), in its input plane by a Fraunhofer transform,

$\begin{matrix}{{{E\text{(}\overset{->}{r}\text{)}} = {\int{{u( \overset{->}{\rho} )}\exp\text{(}{\mathbb{i}\varphi}\text{(}\overset{->}{\rho}\text{)}\text{)}{\exp( {{- {\mathbb{i}}}\;\frac{k{\overset{->}{\; r} \cdot \overset{->}{\rho}}}{2f}} )}{\mathbb{d}^{2}\rho}}}},} & (4)\end{matrix}$where u({right arrow over (p)}) and φ({right arrow over (p)}) are thereal-valued amplitude and phase, respectively, of the field at positionFin the input pupil, and k=2π/λ is the wave number of light ofwavelength λ.

If u({right arrow over (ρ)}) is the amplitude profile of the collimatedlaser used to power the optical trap array, then φ({right arrow over(ρ)}) is the kinoform encoding the pattern. Most practical DOEs,including those projected with SLMs, comprise an array {right arrow over(ρ)}_(j) of discrete phase pixels, each of which can impose any of Ppossible discrete phase shifts φ_(j) ∈ {0, . . . , φ_(P−1)}. The fieldin the focal plane due to such an N-pixel DOE is, therefore,

$\begin{matrix}{{{E\text{(}\overset{->}{r}\text{)}} = {\sum\limits_{j = 1}^{N}{u_{j}{\exp( {\mathbb{i}\varphi}_{j} )}T_{j}\text{(}\overset{->}{r}\text{)}}}},} & (5)\end{matrix}$where the transfer matrix describing the propagation of light from inputplan to output plane is

$\begin{matrix}{{T_{j}\text{(}\overset{->}{r}\text{)}} = {{\exp( {{- {\mathbb{i}}}\;\frac{k{\overset{->}{\; r} \cdot \overset{->}{\rho}}}{2f}} )}.}} & (6)\end{matrix}$Unlike more general holograms, the desired field in the output plan of aholographic optical trapping system consists of M discrete bright spotslocated at {right arrow over (r)}_(m):

$\begin{matrix}{{{E\text{(}\overset{->}{r}\text{)}} = {\sum\limits_{m = 1}^{M}{E_{m}\text{(}\overset{->}{r}\text{)}}}},{with}} & (7) \\{{{E_{m}\text{(}\overset{->}{r}\text{)}} = {{\alpha_{m}\delta\text{(}\overset{->}{r}} - {{\overset{->}{r}}_{m}\text{)}{\exp( {\mathbb{i}\xi}_{m} )}}}},} & (8)\end{matrix}$where α_(m) is the relative amplitude of the m-th trap, normalized byΣ_(m=1) ^(M)|α_(m)|²=1, and ξ_(m) is its (arbitrary) phase. Here,δ({right arrow over (r)}) represents the amplitude profile of thefocused beam of light in the focal plane, which may be treatedheuristically as a two-dimensional Dirac delta function. The designchallenge is to solve Eqs. (5), (6) and (7) for the set of phase shiftsξ_(m), yielding the desired amplitudes α_(m) at the correct locations{right arrow over (r)}_(m) given u_(j) and T_(j)({right arrow over(ρ)}).

The Gerchberg-Saxton algorithm and its generalizations, such as theadaptive-additive algorithm, iteratively solve both the forwardtransform described by Eqs. (5) and (6), and also its inverse, takingcare at each step to converge the calculated amplitudes at the outputplane to the design amplitudes and to replace the back-projectedamplitudes, u_(j) at the input plane with the laser's actual amplitudeprofile. Appropriately updating the calculated input and outputamplitudes at each cycle can cause the DOE phase φ_(j), to converge toan approximation to the ideal kinoform, with monotonic convergencepossible for some variants. The forward and inverse transforms mappingthe input and output planes to each other typically are performed byfast Fourier transform (FFT). Consequently, the output positions {rightarrow over (r)}_(m) also are explicitly quantized in units of theNyquist spatial frequency. The output field is calculated not only atthe intended positions of the traps, but also at the spaces betweenthem. This is useful because the iterative algorithm not only maximizesthe fraction of the input light diffracted into the desired locations,but also minimizes the intensity of stray light elsewhere.

FFT-based iterative algorithms have drawbacks for computingthree-dimensional arrays of optical tweezers, or mixtures of moregeneral types of traps. To see this, one notes how a beam-splitting DOEcan be generalized to include wave front-shaping capabilities.

A diverging or converging beam at the input aperture comes to a focusand forms a trap downstream or upstream of the focal plane,respectively. Its wave front at the input plane is characterized by theparabolic phase profile

$\begin{matrix}{{\varphi_{z}\text{(}\overset{->}{\rho}},{{z\text{)}} = \frac{k\;\rho^{2}z}{f^{2}}},} & (9)\end{matrix}$where z is the focal spot's displacement along the optical axis relativeto the lens' focal plane. This phase profile can be used to move anoptical trap relative to the focal plane even if the input beam iscollimated by appropriately augmenting the transfer matrix:T _(j) ^(z)({right arrow over (r)})=T _(j)({right arrow over (r)})K _(j)^(z)({right arrow over (r)}),  (10)where the displacement kernel isK _(j) ^(z)({right arrow over (r)})=exp(iφ _(z)({right arrow over(ρ)}_(j) ,z)),  (11)and using the result as the kernel of Eq. (5).

Similarly, a conventional TEM beam can be converted into a helical modeby imposing the phase profileφ_(l)({right arrow over (ρ)})=lθ,  (12)where θ is the azimuthal angle around the optical axis and l is anintegral winding number known as the topological charge. Suchcorkscrew-like beams focus to ring-like optical traps known as opticalvortices that can exert torques as well as forces. Thetopology-transforming kernel K_(j) ^(l)({right arrow over(r)})=exp(iφ_(l)({right arrow over (ρ)}_(j))) can be composed with thetransfer matrix in the same manner as the displacement-inducing K_(j)^(z)({right arrow over (r)}). An additional kernel can be incorporatedin the same manner to implement modulated tweezers according to Eq. (2).

A variety of comparable phase-based mode transformations have beendescribed, each with applications to single-beam optical trapping. Allcan be implemented by augmenting the transfer matrix with an appropriatetransformation kernel. Moreover, different transformation operations canbe applied to each beam in a holographic trapping pattern independently,resulting in general three-dimensional configurations of diverse typesof optical traps.

Calculating the phase pattern φ_(j) encoding multifunctionalthree-dimensional optical trapping patterns requires only a slightelaboration of the algorithms used to solve Eq. (5) for two-dimensionalarrays of conventional optical tweezers. The primary requirement is tomeasure the actual intensity projected by φ_(j) into the m-th trap atits focus. If the associated diffraction-generated beam has anon-trivial wave front, then it need not create a bright spot at itsfocal point. On the other hand, if we assume that φ_(j) creates therequired type of beam for the m-th trap through a phase modulationdescribed by the transformation kernel K_(j,m)({right arrow over (r)}),then applying the inverse operator, K_(j,m) ⁻¹({right arrow over (r)})in Eq. (5) would restore the focal spot.

This principle was first applied to creating three dimensional traparrays in which separate translation kernels were used to project eachdesired optical tweezer back to the focal plane as an intermediate stepin each iterative refinement cycle. Computing the light projected intoeach plane of traps in this manner involves a separate Fourier transformfor the entire plane. In addition to its computational complexity, thisapproach also requires accounting for out-of-focus beams propagatingthrough each focal plane, or else suffers from inaccuracies due tofailure to account for this light.

A substantially more efficient approach involves computing the fieldonly at each intended trap location, as

$\begin{matrix}{{{E_{m}\text{(}{\overset{->}{r}}_{m}\text{)}} = {\sum\limits_{j = 1}^{N}{K_{j,m}^{- 1}\text{(}{\overset{->}{r}}_{m}\text{)}T_{j}\text{(}{\overset{->}{r}}_{m}\text{)}{\exp( {- {\mathbb{i}\varphi}_{j}} )}}}},} & (13)\end{matrix}$and comparing the resulting amplitude α_(m)=|E_(m)| with the designvalue. Unlike the FFT-based approach, this per-trap algorithm does notdirectly optimize the field in the inter-trap region. Conversely, thereis no need to account for interplane propagation. If the values of α_(m)match the design values, then no light is left over to create ghosttraps.

Iteratively improving the input and output amplitudes by adjusting theDOE phases, φ_(j), involves backtransforming from each updated E_(m)using the forward transformation kernels, K_(j,m)({right arrow over(r)}_(m)) with one projection for each of the M traps. By contrast, theFFT-based approach involves one FFT for each wave front type within eachplane and may not converge if multiple wave front, types are combinedwithin a given plane. The only adjustable parameters in Eqs. (8) and(13) are the relative phases ξ_(m) of the projected traps. These M−1real-valued parameters must be adjusted to optimize the choice ofdiscrete-valued phase shifts, φ_(j), subject to the constraint that theamplitude profile u_(j) matches the input laser's. This problem islikely to be underspecified for both small numbers of traps and forhighly complex heterogeneous trapping patterns. The result for suchcases is likely to be optically inefficient holograms whose projectedamplitudes differ from their ideal values.

Equation (13) suggests an alternative approach for computing DOEfunctions for discrete HOT patterns. The operator, K_(j,m) ⁻¹({rightarrow over (r)}_(m))T_(j)({right arrow over (r)}_(m)) describes howlight in the mode of the m-th trap propagates from position {right arrowover (ρ)}_(j) Fib on the DOE to the trap's projected position {rightarrow over (r)}_(m), in the lens' focal plane. If we were to change theDOE's phase φ_(j) at that point, then the superposition of rayscomposing the field at {right arrow over (r)}_(m) would be affected.Each trap would be affected by this change through its own propagationequation. If the changes led to an overall improvement, then one wouldbe inclined to keep the change, and seek other such improvements. If,instead, the result were less good, φ_(j) would be restored to itsformer value and the search for other improvements would continue. Thisis the basis for direct search algorithms, including the extensivecategory of simulated annealing and genetic algorithms. These relatedalgorithms differ in their approach to accepting and rejecting candidatechanges, and in their methods for creating such candidates. Here, it isdescribed how to apply these algorithms specifically to HOT CGHcomputation.

In its most basic form, direct search involves selecting a pixel atrandom from a, trial phase pattern, changing its value to any of the P−1alternatives, and computing the effect on the projected field. Thisoperation can be performed efficiently by calculating only the changesat the M trap's positions due to the single changed phase pixel, ratherthan summing over all pixels. The updated trial amplitudes then arecompared with their design values and the proposed change is accepted ifthe overall amplitude error is reduced. The process is repeated untilthe acceptance rate for proposed changes becomes sufficiently small.

The key to a successful and efficient direct search for φ_(j) is toselect a function that effectively quantifies projection errors. Thestandard cost function, Σ_(m=1) ^(M)(I_(m)−∈ I_(m) ^((D)))², assessesthe mean-squared deviations of the m-th trap's projected intensity I,from its design value I_(m) ^((D)), assuming an overall diffractionefficiency of ∈. It requires an accurate estimate for ∈ and places noemphasis on uniformity in the projected traps' intensities. Analternative,C=−

I

+ƒσ,  (14)proposed by Meister and Winfield avoids both shortcomings. Here,

$\langle I \rangle = {\frac{1}{M}{\sum\limits_{m = 1}^{M}I_{m}}}$is the mean intensity at the traps and

$\begin{matrix}{\sigma = \sqrt{\frac{1}{M}{\sum\limits_{m = 1}^{M}( {I_{m} - {\gamma\; I_{m}^{(D)}}} )^{2}}}} & (15)\end{matrix}$measures the deviation from uniform convergence to the designintensities. Selecting

$\begin{matrix}{\gamma = \frac{\sum\limits_{m = 1}^{M}{I_{m}I_{m}^{(D)}}}{\sum\limits_{m = 1}^{M}{\text{(}I_{m}^{(D)}\text{)}^{2}}}} & (16)\end{matrix}$minimizes the total error and accounts for non-ideal diffractionefficiency. The weighting fraction ƒ sets the relative importanceattached to overall diffraction efficiency and uniform convergence.

In the simplest direct search for an optimal phase distribution, anycandidate change that reduces C is accepted, and all others arerejected. Selecting pixels to change at random reduces the chances ofthe search becoming trapped by suboptimal configurations that happen tobe highly correlated. The typical number of trials required forpractical convergence should scale as N P, the product of the number ofphase pixels and the number of possible phase values. In practice, thisrough estimate is accurate if P and N are comparatively small. Forlarger values, however, convergence is attained far more rapidly, oftenwithin N trials, even for fairly complex trapping patterns.

FIG. 2 shows a typical application of the direct search algorithm tocomputing a HOT DOE consisting of 51 traps, including 12 opticalvortices of topological charge l=8, arrayed in three planes relative tothe focal plane. The 480×480 pixel phase pattern was refined from aninitially random superposition of fields in which amplitude variationswere simply ignored. The results in FIG. 2 were obtained with a singlepass through the array. The resulting traps, shown in the bottom threeimages, appear uniform. This effect was achieved by setting the opticalvortices' brightness to 15 times that of the conventional opticaltweezers. This single hologram therefore demonstrates independentcontrol over three-dimensional position, wave front topology, andbrightness of all the traps.

To demonstrate these phenomena more quantitatively, standard figures ofmerit are augmented with those known in the art. In particular, theDOE's theoretical diffraction efficiency is commonly defined as

$\begin{matrix}{{Q = {\frac{1}{M}{\sum\limits_{m = 1}^{M}\frac{I_{m}}{I_{m}^{(D)}}}}},} & (17)\end{matrix}$

and its root-mean-square (RMS) error as

$\begin{matrix}{e_{rms} = {\frac{\sigma}{\max\;( I_{m} )}.}} & (18)\end{matrix}$

The resulting pattern's departure from uniformity is usefully gauged as

$\begin{matrix}{u = {\frac{\max\;( {{I_{m}/I_{m}^{(D)}} - {\min\;( {I_{m}/I_{m}^{(D)}} )}} )}{\max\;( {{I_{m}/I_{m}^{(D)}} + {\min\;( {I_{m}/I_{m}^{(D)}} )}} )}.}} & (19)\end{matrix}$These performance metrics are plotted in FIG. 3 as a function of thenumber of accepted single-pixel changes. The overall acceptance rate forchanges after a single pass through the entire DOE array was better than16%.

FIG. 3 demonstrates that the direct search algorithm trades off a smallpercentage of the overall diffraction efficiency in favor ofsubstantially improved uniformity.

Two-dimensional phase holograms contain precisely enough information toencode any two-dimensional intensity distribution. A three-dimensionalor multi-mode pattern, however, may require both the amplitude and thephase to be specified in the lens' focal plane. In such cases, atwo-dimensional phase hologram can provide at best an approximation tothe desired distribution of traps.

The most straightforward elaboration of a direct search is the class ofsimulated annealing algorithms. Like direct search, simulated annealingrepeatedly attempts random changes to randomly selected pixels. Alsolike direct search, a candidate change is accepted if it would reducethe cost function. Simulated annealing avoids becoming trapped away fromthe globally optimal solution by also accepting some changes thatincrease the cost function, with a probability P that falls offexponentially with the increase ΔC in cost:

$\begin{matrix}{P = {\exp\;{( {- \frac{\Delta\; C}{C_{0}}} ).}}} & (20)\end{matrix}$In this case, C₀ is a characteristic cost that plays the role of thetemperature in the standard Metropolis algorithm used in Monte Carlosimulations. Increasing C₀ results in an increased acceptance rate ofcostly changes. This has the benefit of kicking the phase pattern out ofany local minima so that the globally optimal solution may be found. Theincreased acceptance rate also increases the time required to convergeto that solution, however, and therefore increases the computationalcost of the calculation.

The tradeoff between exhaustive and efficient searching can be optimizedby selecting an appropriate value of C₀. Unfortunately, the best choicemay be different for each application. Starting C₀ at a large value thatpromotes exploration and then reducing it to a lower value that speedsconvergence offers a convenient compromise.

Effective searches may be implemented by attempting to change multiplepixels simultaneously, instead of one at a time. Different patterns ofmulti-pixel changes may be particularly effective for optimizingtrap-forming phase holograms of different types, and the approaches usedto identify and improve such patterns generally are known as geneticalgorithms.

All of these more sophisticated approaches may have applications indesigning high-efficiency, high-accuracy DOEs for HOT applications. Inmany cases of practical interest, the simplest is also the fastest andoffers substantial advantages over previously reported algorithms.

FIG. 8 shows a first implementation of two-color holographic opticaltraps (2C-HOT). In FIG. 8, an objective lens 200 is used to focus lightfrom laser 210 and laser 240 into optical traps, which are intended tobe projected into a sample. For the first the path of laser beam 215emanating from laser 210, the wavefronts of this beam are modulated bythe diffractive optical clement (DOE) 220 before being projected bylenses 225 and 230 to the input plane of objective 200. Lenses 225 and230 should be understood to be any relay optical train accomplishing thetransfer of the modulated beam 215 to the focusing element 200. On itsway to the focusing element 200, beam 215 is redirected by reflectionoff of an element 235, which is either a dichroic mirror, a partiallysilvered mirror, a polarization-selective beam splitter, or the like.For purposes of this application, this element, or any equivalentelement is considered to be a dichroic mirror. The element 235 isdesigned to reflect the laser beam 215 and to transmit other light,either as a function of its wavelength, its polarization, or some otherproperties.

The ability of the element 235 to reflect the HOT-forming laser beam 215while transmitting other light provides the system with the capabilityto form images of the sample being manipulated, the imaging light beingable to pass through the element 235 to a conventional imaging train. Italso provides a method for implementing 2C-HOT.

In the scenario shown in FIG. 8, a second laser 240 projects a secondlaser beam 245, which is operated on by DOE 250. This modified beam 245is relayed by lenses 255 and 260 to the objective 200, and thereby formsholographic optical traps. This second beam 245 is reflected into theinput aperture of the objective 200 by a dichroic 265. This element isdesigned to reflect laser light 245 from the laser 240, and mayoptionally transmit other light. The dichroic 235, by contrast, isdesigned to transmit this light so that it can reach the objective 200and be focused into traps.

It should be emphasized that the beams 215 and 245 need not be generatedby separate lasers, but instead could be created by a single laser beamthat has been split and operated on by other elements, not shown. Also,the DOE's are shown operating in transmission. They might equivalentlybe replaced by reflective DOE's with the necessary modifications to theoptical trains. The DOE's can modulate the phase, amplitude, andpolarization of the incident beams in any way required to createholographic optical traps, and can include computer-addressed spatiallight modulators.

FIG. 9 is a representation of a variant of the design of FIG. 8. In FIG.9, a laser 310 provides a first beam 315, which is operated on by afirst DOE 320 before being relayed by first and second lenses 325 and330 to a focusing element 300 to form optical traps. A first dichroic320 is designed to reflect this trapping light into the focusingelement, and optionally to transmit other light. The first beam 315passes through a beam splitter 360, which also could be a dichroicmirror, a polarization-selective beam splitter or a partially silveredmirror, for example.

The beam splitter 360 is designed to reflect a second beam 345 producedby a second laser 340. The second beam 345 is operated on by a secondDOE 350 to form a second set of holographic optical traps. The modulatedlight is relayed to focusing the focusing element 300 by the combinationof the first lens 325 and a third lens 355, the beam splitter 360, and asecond dichroic 350. Unlike the previous method, the second dichroic 350is designed also to reflect light 345 from the laser 340.

The first and second beams, 315 and 345 travel along the same opticalaxis downstream of the beam splitter 360.

FIG. 10 shows still another variation of the present invention. In thiscase, first and second beams 1415 and 1445 from first and second lasers1410 and 1440 are focused into traps by focusing an element 1400 afterbeing relayed by first and second lenses 1425 and 1430 and beingreflected by a dichroic 1435. The two beams are separately operated onby first and second DOE's 1420 and 1450, as shown. Once modulated by thefirst DOE 1420, the first beam 1415 passes through a beam splitter 1460,whereas the second beam 1445 is reflected by the beam splitter 1460after being operated on by the second DOE 1450. As in the system of FIG.9, the dichroic 1425 is designed to reflect both the first and secondbeams 1415 and 1445 and may transmit other light.

FIG. 11 shows an optical train according to yet another embodiment ofthe present invention. In this embodiment, first and second laser beams1515 and 1545 produced by first and second lasers 1510 and 1540 aredirected onto the same optical axis by a beam splitter 1560 and areoperated on by the same DOE 1520. The two modulated beams then arerelayed by first and second lenses 1525 and 1530 to a focusing element1500, after being reflected by a dichroic 1525. In the case that thefirst and second beams 1515 and 1545 have different wavelengths, thistwo-color DOE can imprint a different phase modulation on each,resulting in two distinct patterns of traps being projected. This DOEmust be calculated specifically to accommodate two distinct beams and,therefore, has additional design considerations when compared with thesingle-wavelength DOE's described in the previous methods.

In some applications, tuning fractionation by visual inspection may beundesirable or impractical. In such instances, an alternativecharacterization method based upon electrical (rather than optical)measurements may be preferable. FIG. 13 schematically depicts arepresentative implementation 1600 of optoelectrokinetic potentiometry.The sample consists of charged objects such as colloidal particles,macroions, or biological cells, which are dispersed in a solvent such aswater. The sample flows at speed ν, along a channel and through the gapbetween two electrodes. No potential will develop across this gap if theelectrodes are arranged transverse to the flow direction, and anelectrometer connected across the electrodes will register no voltage.This is the null condition for this measurement.

A measurement is performed by projecting an array of optical traps 1630into the interelectrode gap. These optical traps 1630 may be created,for example, with a holographic optical tweezer technique, with thegeneralized phase contrast method, or with an interferometricallygenerated optical lattice. Fluid-borne objects experience a structuredpotential energy landscape due to their interaction with the opticalintensity distribution. Depending on their optical properties, they maybe attracted to or repelled by the brightest regions. The followingconsiderations apply to either case.

Particles are able to traverse an array of optical traps 1630 if theviscous drag force due to the flowing fluid exceeds the traps' 1630maximum trapping force. Their trajectories nevertheless are influencedby encounters with these potential wells. If the trap array 1630 isaligned with the driving force, then particles simply hop from well towell along the line, their trajectories somewhat slowed. If, on theother hand, the trap array 1630, is inclined with respect to the flowdirection, then particles can become locked into symmetry-selecteddirections through the potential energy landscape and thus can bedeflected away from the direction of the driving force. This is theprinciple behind optical fractionation as discussed above.

One effect of this deflection is the creation of a component of thecharged particles' velocity directed across the inter-electrode gap.This optically-induced transverse speed, ν_(⊥), leads to a measurableelectrokinetic potential whose magnitude depends on the transverse flowspeed, the charge on the particles, and the particles' hydrodynamicproperties. The relationship between ν_(⊥)and the measured voltagedepends on properties of the particles and their solvent. The sign ofthe voltage depends on the sign of the particles' charge and the sign ofν_(⊥). The magnitude and direction of the transverse velocity depends,in turn, on details of the particles' interaction with the opticalintensity pattern, and on the pattern's geometry. This means that thetransverse voltage measured in this apparatus is sensitive to a widerange of properties in both the particles and their supportingelectrolyte. One can also apply an external bias force 1605 to thesample 1610 which is a plurality of charged particles, orienting anarray of the optical traps 1630 at a plurality of angles with respect tothe bias force 1605 and then measuring the transverse voltage at each ofthe plurality of angles wherein each measurement of the transversevoltage is associated with a corresponding angle of the array at whichthe measurement is made.

FIG. 13 shows representative experimental data obtained for colloidalsilica spheres. This plot shows the transverse velocity ν_(⊥) relativeto flow speed ν of 1.5 μm diameter silica spheres dispersed in water, asa function of orientation angle Θ of a 10×10 array of holographicoptical tweezers. The transverse component of the particles' velocityincreases as the array's orientation increases from Θ=0 (aligned)because particles remain locked in to the [1,0] lattice direction. Oncethe particles become unlocked from this commensurate path through thetrap array, the deflection angle decreases and actually changes sign asthe trajectories become locked in to the diagonal [1,1] direction. Thetransverse voltage measured in the apparatus of FIG. 12 would track thistrend, including the sign reversal.

Given this information obtained over a range of orientations, the signof the measured transverse potential indicates the sign of the flowingparticles' charges. The angle and magnitude of maximum and minimumtransverse voltage can be used to gauge the magnitude of the particles'charges. Their dependence on laser power and the array's latticeconstant can be used to measure the particles' hydrodynamic radius andthe polydispersity in size.

Even a single measurement at fixed orientation can provide informationon the sign of the transported particles' charge. A rapid series ofmeasurements as a function of orientation, laser power, flow speed, trapgeometry, or any combination of these can be used to extract verydetailed information about a spectrum of properties. This approach,therefore, provides more information about a wider range of propertiesthan any other single measurement technique. The measurement is easilyautomated, and could be useful in process control and quality assuranceapplications. It operates naturally on continuous streams, as well as ondiscrete batches, and so could be integrated into manufacturingprocesses.

Electrokinetically assaying of the state of kinetically locked intransport also can be used to optimize optical fractionation of chargedspecies without directly imaging the flowing sample or sampling thedownstream fractions. Consequently, the present invention also providessubstantial benefits for automated optical fractionation.

While several embodiments have been shown and described herein, itshould be understood that changes and modifications can be made to theinvention without departing from the invention in its broader aspects.Various features of the invention are defined in the following Claims.

1. A method for characterizing a charged solute, comprising the stepsof: operatively spacing apart a first electrode and a second electrodeto form an interelectrode gap; providing an electrometer incommunication with the first electrode and the second electrode;projecting an array of optical traps positioned in the interelectrodegap; using the first electrode and second electrode to measure thetransverse electrokinetic voltage arising from the deflection of thecharged solute by the array of optical traps as the charged solute isbeing driven by solvent flow through the array of optical traps; andusing the transverse electrokinetic voltage to characterize the chargedsolute.
 2. In the method of claim 1 wherein an external biasing force ispresent, the improvement, comprising the steps of: applying the externalbiasing force to a plurality of charged particles; orienting the arrayat a plurality of angles with respect to the biasing force; andmeasuring the transverse electrokinetic voltage at each of the pluralityof angles, wherein each measurement of the transverse electrokineticvoltage is associated with a corresponding angle of the array at whichthe measurement is made.
 3. The method of claim 2, further comprisingthe step of determining a maximum transverse electrokinetic voltage, aminimum transverse electrokinetic voltage and the corresponding anglesof the array.
 4. The method of claim 3, further comprising the step ofcalculating the magnitude of the charged particles' charge from themaximum transverse electrokinetic voltage, the minimum transverseelectrokinetic voltage, and the respective corresponding angles of thearray.
 5. The method as defined in claim 1 further comprising the stepof determining magnitude of charge of the solute from the transverseelectrokinetic voltage.
 6. The method as defined in claim 5 wherein thestep of determining magnitude of charge comprises measuring magnitude ofmaximum and minimum values of the transverse electrokinetic voltage. 7.The method as defined in claim 1 further comprising the step ofdetermining a particle hydrodynamic radius for the solute from thetransverse electrokinetic voltage.
 8. The method as defined in claim 7wherein a laser is used to form the array of optical traps and the stepof determining a particle hydrodynamic radius comprises measuringdependence of the transverse electrokinetic voltage on power from thelaser used to form the array of optical traps.
 9. The method as definedin claim 7 wherein the step of determining a particle hydrodynamicradius comprises measuring a lattice constant of the array of opticaltraps.
 10. The method as defined in claim 1 further including the stepof measuring sign of charge for the charted solute by determining signof the transverse electrokinetic voltage.
 11. The method as defined inclaim 1 further including the step of determining polydispersity in sizeof particles of the charged solute by measuring at least one of maximumtransverse electrokinetic voltage, minimum transverse electrokineticvoltage, dependence of the maximum transverse electrokinetic voltage andthe minimum transverse electrokinetic voltage on power of a laser usedto form the optical traps and dependence of the maximum transverseelectrokinetic voltage and minimum transverse electrokinetic voltage onlattice constant of the array of optical traps.
 12. The method asdefined in claim 1 further including the step of determining flowvelocity of the charged solute from measured values of transversevelocity of the charged solute.
 13. The method as defined in claim 1further including the step of measuring as a function of angularorientation at least one of power of a laser used to form the opticaltraps, flow speed of the charged solute, optical trap geometry andcombinations thereof to obtain detailed information about properties ofthe charged solute.